The problem of robustness for truncated sequential tests of two simple hypotheses is considered for the model of heterogeneous independent observations under distortions. An approach for performance characteristics calculation is proposed. Asymptotic analysis of robustness is performed. A family of robustified sequential tests is constructed. Numerical examples illustrate the theoretical results.
{"title":"Robustness of sequential hypotheses testing for heterogeneous independent observations","authors":"A. Kharin, T. Tu","doi":"10.1090/tpms/1104","DOIUrl":"https://doi.org/10.1090/tpms/1104","url":null,"abstract":"The problem of robustness for truncated sequential tests of two simple hypotheses is considered for the model of heterogeneous independent observations under distortions. An approach for performance characteristics calculation is proposed. Asymptotic analysis of robustness is performed. A family of robustified sequential tests is constructed. Numerical examples illustrate the theoretical results.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/tpms/1104","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49078612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hypothesis testing in the Cox proportional hazards model with measurement errors","authors":"O. Chernova","doi":"10.1090/tpms/1107","DOIUrl":"https://doi.org/10.1090/tpms/1107","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/tpms/1107","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44471594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present paper develops a goodness of fit statistic for the linear regression models fitted by the shrinkage type estimators. A family of double k-class estimators is considered as a shrinkage estimator which encompasses several estimators as its particular case. The covariance matrix of error term is assumed to be a non-identity matrix under two situationsknown and unknown. The goodness of fit statistics based on the idea of coefficient of determination in multiple linear regression model is proposed for the family of double k-class estimators. Its first and second order moments up to the first order of approximation are derived and finite sample properties are studied using the Monte-Carlo simulation.
{"title":"Goodness of fit for generalized shrinkage estimation","authors":"Chi-Lun Cheng, Shalabh, A. Chaturvedi","doi":"10.1090/tpms/1106","DOIUrl":"https://doi.org/10.1090/tpms/1106","url":null,"abstract":"The present paper develops a goodness of fit statistic for the linear regression models fitted by the shrinkage type estimators. A family of double k-class estimators is considered as a shrinkage estimator which encompasses several estimators as its particular case. The covariance matrix of error term is assumed to be a non-identity matrix under two situationsknown and unknown. The goodness of fit statistics based on the idea of coefficient of determination in multiple linear regression model is proposed for the family of double k-class estimators. Its first and second order moments up to the first order of approximation are derived and finite sample properties are studied using the Monte-Carlo simulation.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/tpms/1106","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46620522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A limit theorem for sums of independent random elements in a Banach space","authors":"I. Matsak","doi":"10.1090/tpms/1102","DOIUrl":"https://doi.org/10.1090/tpms/1102","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43836227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The model of conditionally binomial nonlinear regression time series with discrete regressors is considered. A new frequencies-based estimator (FBE) of explicit form is constructed for this model. FBE is shown to be consistent, asymptotically normal, asymptotically effective, and to have less restrictive uniqueness assumptions w. r. t. the classical MLE. A fast recursive algorithm is constructed for FBE re-computation under model extension. Asymptotically optimal Wald test and forecasting statistic based on FBE are developed. Computer experiments on simulated data are performed for FBE.
{"title":"Statistical analysis of conditionally binomial nonlinear regression time series with discrete regressors","authors":"Yuriy S. Kharin, V. Voloshko","doi":"10.1090/tpms/1105","DOIUrl":"https://doi.org/10.1090/tpms/1105","url":null,"abstract":"The model of conditionally binomial nonlinear regression time series with discrete regressors is considered. A new frequencies-based estimator (FBE) of explicit form is constructed for this model. FBE is shown to be consistent, asymptotically normal, asymptotically effective, and to have less restrictive uniqueness assumptions w. r. t. the classical MLE. A fast recursive algorithm is constructed for FBE re-computation under model extension. Asymptotically optimal Wald test and forecasting statistic based on FBE are developed. Computer experiments on simulated data are performed for FBE.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/tpms/1105","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45109749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider delayed sums of the type Sn+an − Sn where an is possibly a positive integer valued random variable satisfying certain conditions and Sn is the sum of independent random variables Xn with distribution functions Fn ∈ {G1, G2}. We study the limiting behavior of the delayed sums and prove laws of the iterated logarithm of Chover type. These results extend the results in Vasudeva and Divanji (1992) and Chen (2008).
{"title":"Study of the limiting behavior of delayed random sums under non-identical distributions setup and a Chover type LIL","authors":"M. Sreehari, Pingyan Chen","doi":"10.1090/tpms/1103","DOIUrl":"https://doi.org/10.1090/tpms/1103","url":null,"abstract":"We consider delayed sums of the type Sn+an − Sn where an is possibly a positive integer valued random variable satisfying certain conditions and Sn is the sum of independent random variables Xn with distribution functions Fn ∈ {G1, G2}. We study the limiting behavior of the delayed sums and prove laws of the iterated logarithm of Chover type. These results extend the results in Vasudeva and Divanji (1992) and Chen (2008).","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/tpms/1103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47561408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Properties of a highly reliable system with duplication and exponential failure-free periods of one of the alternating processes","authors":"O. Kushnir, V. Kushnir","doi":"10.1090/tpms/1101","DOIUrl":"https://doi.org/10.1090/tpms/1101","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42641104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We expand the quartic variations in time and the quadratic variations in space of the solution to a stochastic partial differential equation with piecewise constant coefficients. Both expansions allow us to deduce an estimation method of the parameters appearing in the equation.
{"title":"Exact variations for stochastic heat equations with piecewise constant coefficients and application to parameter estimation","authors":"M. Zili, Eya Zougar","doi":"10.1090/tpms/1099","DOIUrl":"https://doi.org/10.1090/tpms/1099","url":null,"abstract":"We expand the quartic variations in time and the quadratic variations in space of the solution to a stochastic partial differential equation with piecewise constant coefficients. Both expansions allow us to deduce an estimation method of the parameters appearing in the equation.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/tpms/1099","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45157365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A generalized Nadaraya–Watson estimator for observations obtained from a mixture","authors":"H. M. Dychko, R. Maiboroda","doi":"10.1090/tpms/1098","DOIUrl":"https://doi.org/10.1090/tpms/1098","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47750887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper an objective Bayesian inference is proposed for the heterogeneity parameter in a generalized marginal random effects model. Models of this kind are widely used in meta-analysis and in ...
{"title":"Noninformative Bayesian inference for heterogeneity in a generalized marginal random effects meta-analysis","authors":"Olha Bodnar","doi":"10.1090/TPMS/1095","DOIUrl":"https://doi.org/10.1090/TPMS/1095","url":null,"abstract":"In this paper an objective Bayesian inference is proposed for the heterogeneity parameter in a generalized marginal random effects model. Models of this kind are widely used in meta-analysis and in ...","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48535190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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